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Initial Boundary‐Value Problems for a Pair of Conservation Laws
Author(s) -
Yong Darryl H.,
Kevorkian J.
Publication year - 2002
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.01429
Subject(s) - conservation law , boundary value problem , mathematics , domain (mathematical analysis) , scale (ratio) , mathematical analysis , boundary (topology) , flow (mathematics) , initial value problem , physics , geometry , quantum mechanics
We describe a multiple‐scale technique for solving the initial boundary‐value problem over the positive x ‐axis for a one‐dimensional pair of hyperbolic conservation laws. This technique involves decomposing the solution into waves and incorporating slow temporal and stretched spatial scales in different parts of the solution domain. We apply these ideas to a wavemaker problem for shallow water flow and show why the presence of source terms in the conservation laws makes the analytic solution more complicated.